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(Investigative Ophthalmology and Visual Science. 2005;46:3712-3717.)
© 2005 by The Association for Research in Vision and Ophthalmology, Inc.
DOI:  10.1167/iovs.05-0266
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Evaluation of the Structure-Function Relationship in Glaucoma

Stuart K. Gardiner, Chris A. Johnson, and George A. Cioffi

From Discoveries In Sight, Devers Eye Institute, Portland, Oregon.


   Abstract
Top
 Abstract
Methods
 Results
 Discussion
 References
 
PURPOSE. While glaucoma is evaluated on the basis of structural and functional test results, the spatial relationship between structure and function is not well defined. This study produces a topographical map to demonstrate how sectors of the optic nerve head (ONH) are related to locations in the visual field, using empiric cross-sectional patient data.

METHODS. One hundred nine subjects with healthy eyes and 166 subjects with diagnosed or suspected glaucoma (one test per patient) were evaluated using a retina tomograph and white-on-white standard automated perimetry (SAP). The tomograph ONH images were divided into 36 sectors; and the sector rim areas normalized to account for changes in the total rim area. These were then correlated with SAP thresholds. For each visual field location, a map was produced indicating the strength of correlation between the normalized sector rim areas and thresholds.

RESULTS. The highest correlation between a sector’s normalized rim area and a SAP location’s sensitivity was 0.520. Twenty-seven of the 52 non–blind spot SAP locations exhibited a correlation greater than 0.2 with at least one ONH sector. Locations in the superior hemifield were usually best correlated with the polar inferior temporal sectors of the ONH; locations in the inferior hemifield were usually best correlated with the polar superior temporal sectors of the ONH.

CONCLUSIONS. A map relating regions of the ONH to SAP test locations has been produced. This map may be useful in elucidating the structure-function relationship, particularly for cases of localized glaucomatous loss.

Primary open-angle glaucoma (POAG) is generally regarded as a progressive optic neuropathy, identifiable by a combination of damage at the optic nerve head (ONH) and/or retinal nerve fiber layer (RNFL) and a reduction in or loss of visual function. POAG is commonly associated with elevated intraocular pressure (IOP) in many patients. Measurement of visual function is usually based on white-on-white standard automated perimetry (SAP) to examine sensitivity thresholds at various locations across the visual field, with characteristic patterns of loss being associated with glaucoma. Examination of the ONH topography can be conducted using a variety of imaging techniques such as the retina tomograph (Heidelberg Retina Tomograph [HRT]; Heidelberg Engineering, GmbH, Heidelberg, Germany) or similar instruments such as the topographic scanning system (TopSS; Laser Diagnostic Technologies, Inc, San Diego, CA), or by computer-assisted measurement of optic disc photographs (planimetry). Although either structural or functional damage can occur without the other developing, it is generally thought that structural damage is detectable before functional loss with the tools currently available.1

Therefore, it has been suggested that diagnoses based on imaging techniques could be made earlier than with SAP. This notion is based on longitudinal studies of glaucoma suspects,2 3 4 5 although these papers are limited by the lack of an objective gold standard for glaucomatous progression. For example, many studies are biased by having inclusion criteria based on initial HRT or SAP test results. The HRT can be used to output various global measures of the ONH, including the volume, area, and maximum and mean depth of the optic cup; the neuroretinal rim volume and area; the disc area; the cup- to disc-area ratio; and a measure of the shape of the cup. These measures have been examined for potential identification of glaucomatous eyes,1 6 7 8 9 10 and have usually been reported to provide good discrimination between diseased and healthy eyes.

However, the exact nature of the relationship between structural (e.g., HRT) measures and functional (e.g., SAP) deficits is not well defined. Several partial maps of the topographic correlations have been published.11 12 13 14 Iester et al.15 found that the superior and inferior 90° sectors were more informative in predicting visual field loss than the temporal or nasal sectors; Gunderseon et al.16 similarly reported that the polar areas of the ONH were more informative for predicting glaucoma. Emdadi et al.17 found that the neuroretinal rim narrowing in the superior and inferior temporal sectors was associated with glaucoma. However, the aim of these studies was to better identify glaucomatous damage; therefore, they provide only low-resolution maps of the structure-function relationship. Although they provide useful information, the areas of the ONH considered are large.

Garway-Heath et al.18 used RNFL defects and prominent bundles to produce a complete map relating SAP test locations to positions of entry into the ONH. They did this by manually tracing the paths along the RNFL from each test location in the visual field toward the ONH, and giving the position of entry in degrees, averaged over several subjects. This produced the first high-resolution map from structure to function. However, this technique was developed to be primarily structural; it does not use any functional (e.g., SAP) data. While it would be expected that there would be a correlation between the visual field test locations and the related positions in the ONH reported in their study, it does not exclude the possibility that other relationships also exist which are not visible on the surface of the RNFL.

The closest method to the one described in this article was a study carried out by Anton et al.13 They calculated the ratio of rim area in 10° ONH sectors to the total rim area, and looked for sectors outside normal limits, all using a confocal scanning laser ophthalmoscope, for 26 patients with focal visual field defects. The procedure described in the present report extends this technique in two fundamental ways. First, it is applied to the entire visual field; second, because the aim of the present study was to determine the topographical structure-function relationship (rather than to identify glaucomatous eyes), the ratio was also adjusted to remove the effect of differences in the total rim area (see Methods). The purpose of this study was to extend the previous work by Anton et al. by performing a detailed comparison of structure (HRT image) and function (SAP) measures.

Each of the global measures derived by the HRT can also be generated per sector, giving further information about the structural properties of the ONH (although some are more useful in this form than others; for example the cup volume in some sectors is sometimes zero in normal eyes). In particular, we chose to examine the neuroretinal rim area, split into sectors. The global rim area measured by HRT or TopSS has been found to be a particularly good predictor of SAP mean deviation1 19 ; a narrowing of the rim correlates strongly with a reduction in threshold contrast sensitivity. However, care must be taken, as the rim area varies even among normal eyes according to such factors as the disc size20 21 and age,22 so it is reasonable to consider normalizing the data in some way to take account of overall generalized changes in the size of the rim.

This study generated a map from structural to functional measures, based on patient data, using 36 10° sectors of the ONH to provide increased resolution.


   Methods
Top
 Abstract
 Methods
Results
 Discussion
 References
 
Data
Individuals with healthy eyes, suspected glaucoma, or a diagnosis of early glaucoma were recruited prospectively. All subjects had been tested on at least one previous occasion with full-threshold white-on-white SAP. Subjects with healthy eyes were recruited at the University of California, Davis. Individuals were selected for inclusion on the basis of achieving an approximately equal frequency distribution of age between the third and seventh decades. Subjects with suspected glaucoma or early glaucoma were recruited from individuals attending Devers Eye Institute, or other office practices in the Portland, Oregon metropolitan area. All subjects were tested at baseline, and the patients with diagnosed or suspected glaucoma were reexamined with both SAP and HRT imaging techniques approximately annually after baseline. The study adhered to the tenets of the Declaration of Helsinki, and all subjects signed an informed consent form before participation in the study.

Inclusion criteria for the healthy-eyes group were a normal anterior segment (slit lamp) and posterior segment (direct ophthalmoscopy), including a physiological ONH appearance on examination by an experienced glaucoma-fellowship-trained ophthalmologist. Exclusion criteria included a history of ocular abnormality, injury, or surgery; family history of glaucoma; the presence of diabetes or other systemic disease known to affect vision; use of medications known to affect vision; best-corrected visual acuity worse than 20/40 (6/12); IOP ≥ 22 mm Hg; spectacle refraction > ±5.00 diopters sphere and/or > ±2.00 diopters cylinder; or unreliable visual field test results.23 To be eligible, both eyes of the subject had to satisfy the above conditions. Note that SAP visual field test status, aside from adequate reliability, did not constitute an entry criterion for inclusion as a subject. One visual field test and HRT evaluation was performed per eye for each subject.

Inclusion criteria for the suspected-glaucoma and early-glaucoma groups included a previously diagnosed glaucomatous optic neuropathy (GON) or suspicious ONH appearance (cup-disc ratio asymmetry > 0.2, potential neuroretinal rim notching or narrowing, disc hemorrhage), and/or ocular hypertension (untreated IOP ≥ 22 mm Hg) in conjunction with at least one of the following risk factors: family history of glaucoma; history of migraine, Raynaud’s syndrome, or vasospasm; African-American ancestry; age > 70 years; or history of systemic hypertension or diet-controlled diabetes. Exclusion criteria for both groups included other previous or current ocular pathology, previous ocular surgery (except successful cataract surgery), best-corrected visual acuity worse than 20/40 in either eye, diabetes requiring medication, and mean deviation on full-threshold program 24-2 SAP > –6 dB.

SAP visual field testing was performed using the Humphrey Field Analyzer (Humphrey Systems, Dublin, California), with a 24-2 pattern and conventional test procedures (Goldmann size III stimulus, 31.5 apostilb or 10 cd/m2 white background, and full-threshold test strategy), an optimal lens correction placed before the tested eye, and the fellow eye occluded with an eye patch.24 Ocular imaging was performed using the HRT, with results based on the mean of three 15° field of view scans centered on the optic disc judged to be of acceptable quality.25 Experienced technicians outlined the margin of the optic disc while viewing stereo photographs.

To be included in this study, the SAP and HRT tests had to be conducted within 21 days of each other. When more than one pair of tests were eligible for a patient, the pair showing the most severe defect (as measured by the mean sensitivity) was used; therefore, only one SAP and one HRT test per patient were included. In total, 166 tests (comprising a 24-2 SAP test and an HRT image) from patients with early glaucoma, ocular hypertension, or GON were included in the study. The HRT was used to output data about optic disc measurements divided into 36 10° sectors. The healthy-eye database was based on 218 tests from 109 subjects (i.e., one test for each eye per subject).

Analysis
The healthy eye data were used to develop a model of the shape of a healthy optic disc. For each healthy eye, the proportion of the total rim area that fell into each of the 36 ONH sectors was calculated (i.e., the rim area for that sector divided by the total rim area). These proportions were then averaged over all 218 eyes. This gave the proportion of the total rim area Ei that would be expected to be within a certain sector i if the eye were healthy; the sum of the Ei is therefore equal to exactly 1.

For each eye in the glaucoma dataset (consisting of data from subjects with suspected or early glaucoma), the rim area for each sector Ri was divided by these normal values, giving a number Ni = Ri/Ei indicating how much larger or smaller the sector rim area was than the average healthy eye (for example a value of Ni = 2 would indicate that sector i is twice the size found in the mean healthy eye; the expected value of Ni would then be 2 for every sector). These Ni were ranked, and normalized by dividing by that value in the 24th-ranked sector (i.e., the 24th-largest value Ni); this removes the effect of the whole rim being larger or smaller than usual. Note that the 24th-ranked sector was chosen by testing all possible quantiles for the normalization, and looking for the best results, as described below. Next, 1 was subtracted from the resulting value for each sector, so that the 24th-ranked sector now had a measure of 0; this produces no effect on the model other than making the programming and interpretation easier, because it will not change the correlations between these measures and SAP sensitivities. So, for each sector i, a sector rim area measure (SRAM) is obtained:

Note that in theory, a healthy eye would have SRAMi = 0 for all sectors. A negative value indicates that the rim is narrower in that sector than would be expected.

For each of the 52 non-blind spot locations in the 24-2 SAP visual field, the correlation between the threshold sensitivity at that location and each SRAMi was calculated within the glaucoma dataset. The ONH sectors that were most highly correlated with that location in the visual field were then determined. An overall measure was defined by taking the five highest correlations to ONH sectors for that location, summing these, and then summing over all 52 locations. The formula for SRAMs given above (and in particular, the choice to normalize on the 24th-ranked sector) was chosen to maximize this measure.


   Results
Top
 Abstract
 Methods
 Results
Discussion
 References
 
For the 218 eyes in the healthy dataset, the mean SAP sensitivity (averaged over the 52 non-blind spot locations in the 24-2 visual field) was 30.6 dB (min 26.6 dB, max 33.5 dB). The mean total rim area was 1.59 mm2 (min 0.94 mm2, max 2.37 mm2). For the 166 eyes in the glaucoma dataset, the mean SAP sensitivity was 28.0 dB (min 13.5 dB, max 33.0 dB); and the mean total rim area was 1.30 mm2 (min 0.39 mm2, max 2.36 mm2).

Figure 1 shows the percentage of the total rim area that fell into each ONH sector, averaged over all 218 healthy eyes, i.e., Ei * 100%. The rim was narrowest near the temporal horizontal meridian; this can be seen to the left in Figure 2 . The rim was at its widest in the polar regions.



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  		FIGURE 1. The proportion of the total ONH rim area falling into each 10°-wide sector, as averaged over the healthy eyes. Sectors are numbered as in the HRT, starting with sector 1 at the horizontal temporal meridian, then rotating superiorly; e.g., sector 10 is the first 10° nasal from vertically upward.

 


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  		FIGURE 2. (A) An image of the ONH of one of the eyes in the study. (B) The sectors of the ONH most closely correlated with the SAP sensitivity at one particular location (9° nasal, 3° inferior); the darker a sector is shaded, the higher the correlation, according to the same key given in Figures 3 and 4 . The temporal region of the ONH is to the left in both parts of the figure.

 
Individual ONH sector–SAP location correlations among the glaucoma dataset ranged from –0.246 to 0.520 (mean 0.051). The best sector correlation at each SAP location ranged from 0.120 to 0.520 (mean 0.277). From examining the resultant maps of structure to function (as in Fig. 3 ), SRAMs discriminated better between those sectors that were good correlates and those that were not, as evidenced by a clearer, less noisy map, compared with maps generated using, for example, non-normalized data. The correlations between total rim area and the sensitivity at each location ranged from 0.10 to 0.27 (mean 0.18). These were, as would be expected, significantly lower than the correlations with the best sector for each location (paired t-test, P = 0.0003).



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  		FIGURE 3. The ONH sectors correlated with the SAP contrast sensitivity threshold at each location in the 24-2 visual field. Each circle represents the correlation map (as in Fig. 2 ) for one location in the visual field, with ONH sectors shaded according to the strength of the correlation to the threshold at that location (key at bottom left). White sectors have a correlation <0. The temporal direction on the ONH is to the left (T in the example ONH at top left), nasal (N) to the right, superior (S) upward, and inferior (I) downward. This should not be confused with the temporal direction of the visual field, which is to the right.

 
Figure 2A shows a sample ONH image from one of the patients in the study, given for reference purposes. Figure 2B shows the correlation map for one location in the visual field (9° nasal, 3° inferior). The darker a sector is shaded, the higher the correlation between the sensitivity at that location and the SRAMs for that sector of the ONH. At this particular visual field location, sectors toward the top left of the ONH are the most closely related to the sensitivity.

Figure 3 shows this correlation map for each location in the visual field, with the locations arranged as in a 24-2 visual field printout. Again, the darker a sector is shaded, the larger the correlation; i.e., the darker-shaded sectors are those most closely related to that location in the visual field. White sectors have a negative correlation. Figure 4 is a simplified version of Figure 3 , with only the five best-correlated sectors shown.



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  		FIGURE 4. The five ONH sectors best correlated with the SAP contrast sensitivity threshold at each location in the visual field. Each circle represents the ONH, as in Figure 3 . The edge of the circle for each location is thickened in the sector corresponding to the entry points of nerve fiber bundles into the ONH found by Garway-Heath et al.18

 
Note that care must be taken when interpreting Figures 3 and 4 , because of possibly confusing directions; light projected to locations in the superior nasal section of the visual field (top left in Figs. 3 and 4 ) will strike the inferior temporal region of the retina, and hence the corresponding sectors would be expected to be in this sector of the ONH.


   Discussion
Top
 Abstract
 Methods
 Results
 Discussion
References
 
In the majority of cases, the ONH sectors that were most highly correlated with the sensitivity of a given visual field location conformed to expectations based on the map from Garway-Heath et al.18 ; these expectations are shown by the thickened circle rim at each location in Figure 4 . Locations in the superior visual hemifield tend to be most highly correlated with the inferior and slightly temporal area of the ONH (roughly between 5 and 8 o’clock for a right eye); locations in the inferior visual hemifield tend to be most highly correlated with the superior and slightly temporal area of the ONH (between approximately 10 and 12 o’clock for a right eye). This agrees with the results from Emdadi et al.17 A small degree of crossover of the horizontal meridian is apparent; i.e., locations immediately adjacent to the horizontal meridian exhibit some correlation with the area of the ONH that would otherwise be expected to be related only to locations in the other hemifield. This might be explained by the fact that the meridian in the RNFL will not always be exactly horizontal; this theory is supported by the observation that these crossover correlations at locations along the horizontal meridian become slightly stronger further from fixation. The best-correlated sectors tended to be slightly nearer vertical than the entry points into the ONH of corresponding retinal nerve fiber bundles found by Garway-Heath et al.18

This method produced good results in most of the superior hemifield, with a clear (and expected) pattern apparent in Figure 3 . In the inferior hemifield, the pattern is less clear but still marked. At locations nearer the blind spot, results are less impressive, particularly in the inferior hemifield; no sectors here showed particularly high correlations with the sensitivities. This may be because there were fewer eyes in the dataset with defects in this area; for example only 1% of the eyes had a sensitivity below 25 dB at the inferior temporal location (3°, 3°; between fixation and the blind spot), whereas 3% of eyes had a similarly low sensitivity at the superior temporal location (3°, 3°).

A curious result is the appearance of peripheral superior temporal locations (toward the top right in Fig. 3 ). Sectors between 30° and 70° superior of the temporal meridian were very good predictors of these locations, and also of many inferior locations (which would be more expected); note the similarities between the maps in the top right corner and those near the bottom in Figure 3 . This similarity remained when testing variants on the technique described in this article, including normalizing on a different sector (instead of the 24th-ranked sector) and using the total deviation or pattern deviation instead of the raw sensitivity values for the SAP data. Indeed, the raw sensitivity values of these peripheral superior locations were better correlated to the sensitivities at locations in the inferior hemifield than they were to more central locations in the superior hemifield.

As is usual with any such study, the results are accompanied by caveats. The conclusions are entirely dependent on the data used, and artifacts of the data that are not true effects may appear; it is very possible that the appearance of peripheral superior temporal locations is such an artifact, caused by the locations of defects in eyes in the study. The limited range of sensitivities at some locations mentioned above may also adversely affect the results; a wider range of sensitivities (obtained from a larger dataset) would be expected to improve the results. This is why when multiple pairs of tests (SAP and HRT within 21 days of each other) were available for a patient, the pair with the worst SAP mean sensitivity was chosen; this increases the range of sensitivities. Using a randomly chosen field for each patient resulted in lower correlations. Because the patients included in this study had early glaucoma at worst, and some had only glaucomatous optic neuropathy or suspicious ONH appearance, this should not result in a sample biased toward severe glaucoma. It is further possible that the inclusion/exclusion criteria biased the results; although there is no reason to suspect that such bias would favor some sector-location correlations over others.

The purpose of this study was to determine which sectors of the ONH were best correlated with individual SAP locations. The purpose was not to accurately determine those correlations; the appearances of Figures 3 and 4 are of greater interest than the actual numerical values used to generate them. A number of details of the method used quantitatively changed all the sector-location correlations, but because they did not qualitatively change the assessment of which correlations were stronger than others, those details have been left in their simplest form. One such effect is that changes in the total rim area may be indicative of a change in the SAP sensitivity, which would be removed by the normalization process; however, such information would not aid identification of which individual sectors are best correlated with each SAP location, which is the aim of this study. The data presented here were found to give the best graphical representation for distinguishing well-correlated sectors, inasmuch as it was easier to discern patterns. Results of analyses of the data without undergoing normalization, or using pattern deviation instead of raw sensitivity values, both negatively affected this discriminatory ability, and so they have not been included here (these results are available on request).

Of more concern are factors that could affect some sectors of the ONH more than others. The HRT-defined rim area includes blood vessels, more so in some sectors than others; glaucomatous loss will cause a smaller relative change in the rim area of sectors with a substantial blood vessel component. This may reduce the correlations to sectors slightly nasal of the vertical meridian in either direction, which typically contain large blood vessels. Such sectors rarely appear among the five best-correlated sectors per location in Figure 4 .

Also, although we found no statistically significant difference, it cannot be ruled out that some sectors may have a higher interindividual variability than others; it has been suggest that infero- and superotemporal sectors have lower intereye variability in normal subjects.26 If this were true it would be expected to increase the correlations at those sectors with a lower variability, compared with other sectors. Another sector-dependent problem could be the correlation between the rim areas of adjacent sectors, causing relationships to appear with ONH sectors that are merely close neighbors of the responsible sector; this would be expected to result in the well-correlated areas appearing wider (i.e., comprising more sectors of the ONH) than they actually are. It is our belief that these effects cannot fully account for the strength of the relationships apparent in Figures 3 and 4 ; however, the results should be treated with caution.

The glaucoma dataset for this study contained a mixture of glaucoma suspects and early glaucoma patients. It is possible that with more advanced glaucoma patients, the structure-function relationship could be clearer. Many of the eyes tested exhibited no significant visual field defect with SAP. It would be expected that the inclusion of these eyes in the study would reduce all the structure-function correlations uniformly. However, excluding them would have greatly reduced the sample size, hence making the results less reliable and Figures 3 and 4 less clear. We have found no evidence that removing these eyes would change the qualitative assessment of which areas of the ONH are related to which areas of the visual field.

These results indicate that narrowing of the neuroretinal rim in some areas is more significant than in others, in terms of predicting functional loss; in particular in the polar areas of the ONH. This may account for some of the limitations of predictive power of global HRT indices.


   Acknowledgements
 
The authors thank Balwantray Chauhan (Dalhousie University, Halifax, Nova Scotia, Canada) for his useful comments during the preparation of this manuscript.


   Footnotes
 
Supported by NEI Research Grant EY-03424 (CAJ) and the Oregon Lions Sight and Hearing Foundation (CAJ).

Submitted for publication March 1, 2005; revised April 22 and June 17, 2005; accepted August 22, 2005.

Disclosure: S.K. Gardiner, None; C.A. Johnson, None; G.A. Cioffi, None

The publication costs of this article were defrayed in part by page charge payment. This article must therefore be marked "advertisement" in accordance with 18 U.S.C. §1734 solely to indicate this fact.

Corresponding author: Stuart K. Gardiner, Discoveries In Sight, 1225 NE 2nd Avenue, Portland, OR 97208-3950; sgardiner{at}discoveriesinsight.org.


   References
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 Methods
 Results
 Discussion
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A. Ferreras, L. E. Pablo, D. F. Garway-Heath, P. Fogagnolo, and J. Garcia-Feijoo
Mapping Standard Automated Perimetry to the Peripapillary Retinal Nerve Fiber Layer in Glaucoma
Invest. Ophthalmol. Vis. Sci., July 1, 2008; 49(7): 3018 - 3025.
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T. Jehle, K. Wingert, C. Dimitriu, W. Meschede, J. Lasseck, M. Bach, and W. A. Lagreze
Quantification of Ischemic Damage in the Rat Retina: A Comparative Study Using Evoked Potentials, Electroretinography, and Histology
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H. Cheng, M. Laron, J. S. Schiffman, R. A. Tang, and L. J. Frishman
The Relationship between Visual Field and Retinal Nerve Fiber Layer Measurements in Patients with Multiple Sclerosis
Invest. Ophthalmol. Vis. Sci., December 1, 2007; 48(12): 5798 - 5805.
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R. S. Harwerth, A. S. Vilupuru, N. V. Rangaswamy, and E. L. Smith III
The Relationship between Nerve Fiber Layer and Perimetry Measurements
Invest. Ophthalmol. Vis. Sci., February 1, 2007; 48(2): 763 - 773.
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N. G. Strouthidis, V. Vinciotti, A. J. Tucker, S. K. Gardiner, D. P. Crabb, and D. F. Garway-Heath
Structure and Function in Glaucoma: The Relationship between a Functional Visual Field Map and an Anatomic Retinal Map
Invest. Ophthalmol. Vis. Sci., December 1, 2006; 47(12): 5356 - 5362.
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H. V. Danesh-Meyer, S. C. Carroll, J. Y. F. Ku, J. Hsiang, B. Gaskin, G. G. Gamble, and P. J. Savino
Correlation of Retinal Nerve Fiber Layer Measured by Scanning Laser Polarimeter to Visual Field in Ischemic Optic Neuropathy
Arch Ophthalmol, December 1, 2006; 124(12): 1720 - 1726.
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C. Bowd, L. M. Zangwill, F. A. Medeiros, I. M. Tavares, E. M. Hoffmann, R. R. Bourne, P. A. Sample, and R. N. Weinreb
Structure-function relationships using confocal scanning laser ophthalmoscopy, optical coherence tomography, and scanning laser polarimetry.
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